Talk:Lucas number
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Return type
Q: Why not use UInt64 as return type for the function. It should be the same on all platforms.
Remark: It seems a bit strange to me to derive Lucas(n) from Fib(n), because the Fibonacci sequence is just a special case of the Lucas numbers (with starting values 1,1). —Bart (talk) 19:15, 10 November 2018 (CET)
Here's an example of what I mean:
{
A more general form of the Lucas series, where the 2 starting values
can be set using parameters
}
function LucasGen(L1, L2, N: UInt64): UInt64;
var
i, LucMin1, LucMin2: UInt64;
begin
if (N = 0) then
Raise ERangeError.Create('Lucas function is undefined for 0.');
if (N = 1) then
Exit(L1)
else if (N = 2) then
Exit(L2)
else
begin
LucMin1 := L2;
LucMin2 := L1;
i := 2;
while (i <> N) do
begin
Inc(i);
Result := LucMin2 + LucMin1;
LucMin2 := LucMin1;
LucMin1 := Result;
end;
end;
end;
function Lucas(N: UInt64): UInt64;
begin
Result := LucasGen(2,1,N);
end;
function Fib(N: UInt64): UInt64;
begin
Result := LucasGen(1,1,N);
end;
—Bart (talk) 19:25, 10 November 2018 (CET)
I tried to add the lookup tables here, but the wiki insists that they are spam. ;-)
- A: Yeah, I have a general preference for the CPU's native integer size. Unlike Delphi or GPC, FPC's
integer
/cardinal
is always of fixed width, so I usednativeUInt
. (However, according to its documentation, it's only either 32- or 64-bits, no more, no less, so I can't put code in there for other case.) I just wanna raise awareness for such issues (although it is potentially confusing, hence your question). I, of course, would have writtenuInt64
, too, specificallyqword
, since the former isn't mentioned in the Reference Guide but the latter is. - Don't ask me, but Djzepi created both Fibonacci number and Lucas number. However, I guess it's the other way around: I regard Fibonacci as a general case, and Lucas being a specialization. He introduced calculation of Lucas numbers based on Fibonacci in the page's initial version.
- Regarding your code: I want to keep it simple, the examples in the wiki. This implies:
- I don't wanna assume one is in
{$mode objFPC}
(extended syntax ofexit
routine). - Has
{$modeSwitch exceptions+}
(implicitly set by{$mode objFPC}
or{$mode Delphi}
), and wants them. - Has
{$modeSwitch result+}
(implicitly set by{$mode objFPC}
or{$mode Delphi}
).
- I don't wanna assume one is in
- Therefore I regard my implementation as *the best*. (Surprise!) No. Kidding aside, but seriously, I think it is important to embrace robustness of routines, a general notion I derive from Pascal's strictness. You can discern this in
lucasLeftInverseRange
. In conjunction with{$rangeChecks on}
an out-of-range error can be easily detected (during development). —Kai Burghardt (talk) 20:25, 11 November 2018 (CET)- OK, I see. I consulted Wikipedia; I stand corrected. You're right, Lucas sequences being the generic case, and Fibonacci a special case. However,
if (N = 0) … 'Lucas function is undefined for 0.'
, well, hell yeah it's defined [math]\displaystyle{ n=0 }[/math]. It's been all implementations oflucas
like that. —Kai Burghardt (talk) 20:38, 11 November 2018 (CET)- I'm off by one then. —Bart (talk) 23:05, 11 November 2018 (CET)
- You otherwise agree? My answer isn't like a set in stone argument, but a “plea” for a certain policy.
- I especially like the
relativePosition
in the iterative implementation offibonacci
producing, IMHO, really readable and comprehensible code. —Kai Burghardt (talk) 00:40, 12 November 2018 (CET)- No, I don't agree (talking about the use of NativeInt here). It makes the example unnecessarily complex, IMHO. But it's perfectly fine to disagree on that. —Bart (talk) 18:41, 12 November 2018 (CET)
- OK, so here's the new implementation. It's zero-based, and allows for negative indices.
type LucasRange = -90..90; FibRange = -92..92; function LucasGen(L0, L1, N: Integer; AllowNegativeIndex: Boolean = False): Int64; var i: Integer; LucMin1, LucMin2: Int64; IsNegative: Boolean; begin IsNegative := (N < 0); if (not AllowNegativeIndex) and IsNegative then Raise ERangeError.Create('Range check error: to allow for negative indexes in LucasGen(), you must set the AllowNegativeIndex parameter to TRUE.'); N := Abs(N); if (N = 0) then begin Result := L0 end else if (N = 1) then begin Result := L1 end else begin LucMin1 := L1; LucMin2 := L0; i := 1; while (i <> N) do begin Inc(i); Result := LucMin2 + LucMin1; LucMin2 := LucMin1; LucMin1 := Result; end; end; if IsNegative and Odd(N) then Result := -Result; //(Lucas(-N) = (-1^N)*Lucas(N); end;
- Just for fun. —Bart (talk) 19:47, 13 November 2018 (CET)
- Yeah, I see, it isn't really part of the problem, of the task: “calculate n-th Lucas number”. On the other hand, I wanna write examples, promote code, which you actually would see in a production program. I don't wanna put Pascal in a teaching bubble, as its reputation used to be. I'd leave it as it is, although isn't explained on the page. —Kai Burghardt (talk) 22:34, 15 November 2018 (CET)
- No, I don't agree (talking about the use of NativeInt here). It makes the example unnecessarily complex, IMHO. But it's perfectly fine to disagree on that. —Bart (talk) 18:41, 12 November 2018 (CET)
- I'm off by one then. —Bart (talk) 23:05, 11 November 2018 (CET)
- OK, I see. I consulted Wikipedia; I stand corrected. You're right, Lucas sequences being the generic case, and Fibonacci a special case. However,